User talk:Harold

A collection of thoughts on Morse theory

I'm currently trying to figure out why in Morse homology, the degree of the attaching map of a certain $n$-cell is somehow equivalent to the number of gradient flow lines. The setup is as following. Let $(M, g)$ be a closed (i.e., compact and connected) smooth Riemannian manifold (without boundary), and suppose $f: M \to \mathbb{R}$ is a smooth map satisfying the following properties:

1. for each $x \in \mathrm{Crit}(f) := { p \in M : df_p = 0 }$, the Hessian $\mathrm{Hess}(f): T_pM \times T_pM \to \mathbb{R}$ is non-degenerate. TODO Define the Hessian.
2. $f|_{\mathrm{Crit}(f)}: \mathrm{Crit(f)} \to \mathbb{R}$ is injective.

Caveat with xymatrix

Hey, try this page:

• /Xymatrix caveat

See how you can scroll right? Alec (talk) 22:08, 14 February 2017 (UTC)

Some copy-and-paste-help

It's good to render diagrams in tables, if only because they look a bit sparse with the white background (unless they're huge), try these:

$$\text{YOUR MATH HERE}$$
Comment

To float to the right:

$$\xymatrix{A \ar[r]^f & B}$$
Comment

Now you can write here and reference the diagram on the right

• Lists and everything
  • Baby

Hope it helps Alec (talk) 22:15, 14 February 2017 (UTC)